Marginal Analysis of Point Processes with Competing Risks
Cook, R. J., Chen, B. E. and Major, P.
Handbook of Statistics, Vol. 23.
Point process data arise in medical research when a clinically important event may recur
over a period of observation. Examples are ubiquitous and arise in settings such as
oncology (Gail et al., 1980; Byar et al., 1986; Hortobagyi et al., 1996), cerebrovascular
disease (Hobson et aL, 1993; OASIS, 1997), osteoporosis (Riggs et al., 1990), and
epilepsy (Albert, 1991). Interest typically lies in understanding features of the event
process such as intensity, rate, or mean functions, as well as related group differences
and covariate effects. The method of analysis for point process data is naturally driven
by the feature of interest. Andersen etal. (1993) focus on intensity-based methods for
counting processes, while others emphasize models with a random effect formulation
(Thall, 1988; Abu-Libdeh et al., 1990; Thall and Vail, 1990), marginal methods for
multivariate survival data (Wei et al., 1989), or marginal models based on rate functions
(Lawless and Nadeau, 1995). Interpretation and fit are key factors which help
guide the analysis approach for a given problem, and the merits of the various strategies
have been actively discussed in the literature (Lawless, 1995; Wei and Glidden, 1997;
Cook and Lawless, 1997 a; Oakes, 1997; Therneau and Hamilton, 1997; Cook and Lawless,
2002). Often marginal rate functions serve as a meaningful basis for inference and
these will serve as the focus here.
Frequently when subjects are at risk for recurrent events, they are also at risk for a
so-called terminal event which precludes the occurrence of subsequent eVi;mts. Death,
for example, is a terminal event for any point process generated by a chronic health condition.
The presence of a terminal event with point process data raises challenges which
must be addressed if interest lies in the mean function (Cook and Lawless, I 997b ), the
cumulative distribution function for the number of events over a fixed interval or a lifetime
(Strawderman, 2000), or other aspects of the process. The purpose of this article is
to describe methods of analysis for point process data in the presence of terminal events
while emphasizing connections with methodology for the competing risks problem in